Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−
<em><u>Answer:</u></em>
vertex = (-4, -5)
Axis of symmetry = -4
use the (-4, -5) to find the minimum value
![Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5](https://tex.z-dn.net/?f=Domain%20%3D%20%28%20-%20%5Cinfty%2C%20%5Cinfty%20%29%20%2C%20%5B%20x%20%7C%20x%5C%20is%5C%20real%20%5D%5C%5C%5C%5CRange%20%3D%20%5B%20-5%2C%20%5Cinfty%20%29%2C%20y%5Cgeq%20-5)
<em><u>Solution:</u></em>
Given function is:

The equation in vertex form is given as:

Where, (h, k) is constant
On comparing give function with vertex form,
h = -4
k = -5
Vertex is (-4 , -5)
Axis of symmetry : x co-ordinate of vertex
Thus, axis of symmetry = -4
The coefficient of x^2 is positive in given function.
Thus the vertex point will be a minimum



On comparing,
a = 1
b = 8


Thus, use the (-4, -5) to find the minimum value
Domain and range

The domain is the input values shown on the x-axis
The range is the set of possible output values f(x)
Therefore,
![Domain = ( - \infty, \infty ) , [ x | x\ is\ real ]\\\\Range = [ -5, \infty ), y\geq -5](https://tex.z-dn.net/?f=Domain%20%3D%20%28%20-%20%5Cinfty%2C%20%5Cinfty%20%29%20%2C%20%5B%20x%20%7C%20x%5C%20is%5C%20real%20%5D%5C%5C%5C%5CRange%20%3D%20%5B%20-5%2C%20%5Cinfty%20%29%2C%20y%5Cgeq%20-5)